Monday, 7 August 2017

Antifragility and justice

Towards the end
of last week I noticed a flotsam on my Twitter feed coming from a
storm involving NN Taleb and the prominent British classisist Prof
Beard. The origins were in a BBC schools animation
that depicted a Roman soldier as dark skinned. This elicited a
response on Infowars that the BBC was re-writing history. I was
interested in this because that week my family had driven down to the
Vindolanda and Roman Army Museums on Hadrian’s Wall and I had
been struck that a significant portion of the garrison at Vindolanda
came from Hama in Syria, a region familiar today as being a source of
refugees into Europe. Taleb
was attacking Beard for being part of the conspiracy. Since the
evidence for Syrians at Vindolanda comes from written
records discovered in the 1970s, I cannot believe the ‘left’
are that competent at formulating such a clever consipiracy.

[PS there are links between Financial Mathematics and the mathematics of population genetics: Alison Etheridge
is prominent in both fields. My gut instinct was the apparent lack of
non-Caucasian genes in the current British population was not evidence
of their having been non-Caucasian Romans in Britain. @mpigliucci explains this and highlights how Taleb is a victim of his own biases.]

I was also
interested because Taleb was involved. Along with many academic
mathematicians working on finance I do not have a strong affinity
with Black Swan or Fooled by Randomness. The reason why is as
follows. Taleb, along with other ‘public’ financial
mathematicians like Elie
Ayache and Doyne
Farmer, were part of a cohort of applied mathematicians,
engineers and physicists who entered finance in the 1970s and 1980s,
were successful, became rich and have used that wealth to direct
public perceptions of financial mathematics. At the time, option
pricing was accomplished by solving partial differential equations
and these ‘quants’ had expertise rooted in dynamical –
deterministic – systems (note that Taleb’s mathematical PhD in Management Science was awarded in
1998, not before he went into Finance with an MBA). There is a sense
amongst most actuaries and financial mathematicians, trained in
probability theory, that Taleb’s books resonate with this audience
because the books highlight the significance of randomness, something
these people were not really educated in. As one senior British
actuary said to me: “What does Taleb think actuarial science has
been concerned with for 300 years if not Black Swans and not being
Fooled by Randomness”. This frustration reflects decades of
‘quants’ in banks regarding actuaries as being ponderous
dinosaurs.

A profile
of Taleb by Malcolm Gladwell (who shares Taleb’s skill for
simplification) suggested that Taleb’s ideas are founded on his
experiences of the Lebanese civil war and surviving cancer. While
Taleb dismisses this I wonder if there is some truth in the theory.
Taleb is concerned with how people face up to uncertainty and how
they respond, discussed most recently in Antifragile. I share this
concern but have been dissatisfied with Taleb's arguments, in
particular I feel that Taleb believes,
like many of his colleagues, that there are individuals peculiarly
able to make judgements under uncertainty. This was part of the
motivation for writing Ethics in Quantitative Finance.

My reasoning is
based in mathematics, which is subtly different to Taleb's which just
uses mathematical symbolism. Consider a closed system of 100 agents,
each initially endowed with $45. Now, at each time step each agent
randomly gives another agent $1. What do you think the distribution
of money should be? The immediate thought might be the distribution
would remain uniform, with a little noise. However, this not the
case, as presented in
a nice simulation. Some people will end up with lots of money,
others will be bankrupted. The rich can become rich simply through
luck, not skill. This should not perturb the likes of NN Taleb or
Robert
Mercer, since the model does not consider how genius might skew
the distribution, extending the right tail at the expense of the
middle. It is more challenging to the 'left' who might seek to
implement policies that make the wealth distribution more uniform,
since such policies might be considered to be equivalent to pushing
water up hill.

Moving on, there
are some points that were made with respect to my last post about
maths in economics that are important in understanding my approach.
One
comment was that

The more fatal weakness of this line of argument seems to me the
starting assumptions: mathematics involves "identifying how we
see relations between objects." That seems right, but left
undefined here is the term "objects." What exactly is an
object?

In mathematics, an object is something we can
quantify. Now comes the problem: in economics, what we need to
identify is the relation between emotions (greed, fear of loss,
investor euphoria, etc.) and behavior (buying, selling, tolerance for
risk, and so forth).

Alas, this requires that we
mathematize emotions. To my knowledge, no one has succeeded in doing
this in some 8,000 years of recorded history.

I take a less pessimistic view. Plato split the soul into three
parts. The epithymetikon (‘from the heart’) was the part
of the soul concerned with carnal desires, sometimes represented as a
black horse. Alongside this was the thymoeides (‘spirit’)
and represented energy and the motivation to act, this was sometimes
represented as a white horse. The third component was the logistikon
(‘reason’, from logos the Greek for ‘what is said’) or nous
(‘mind’) that distinguishes right from wrong, which Plato
associated with the Athenian temperament. The logistikon was
sometimes represented as a charioteer controlling the other parts of
the soul, making sure that the spirit would not become dominated by
carnal desires, which would be wrong. Through the medieval period
these ideas became refined into one of balancing passions and
interests. This did not involve quantification, which is only a
small part of mathematics, but by identifying a balance point, which
involves measurement. Adam Smith's great contribution, according
to Albert Hirschman, was in enabling the quantification of
passions and interests through money, precipitating capitalism tied
up with utility maximisation. My argument in EQF is that part of the
long story of financial mathematics is concerned with this balancing
of passions and interests and this was considered to be a question of
Justice. This predates Smith's quantification of passions and
interests,. When mathematics was dominated by geometry, this was
considered in terms of proportions, but with monetisation came
arithmetic.

Justice, according to Socrates and taken up by Plato and Aristotle
and their heirs, is the quality that a complex, functionally
differentiated system (a society) needs to enable it to work well.
On this basis a society is Just when it enables individuals, who all
have different capacities and capabilities, in the society to do
their best by allowing them to do what they are best at. This
relates to comments relating to the use of mathematics in economics
raises, that people are different and so cannot be reduced to a
mathematical representation (e.g. "The rigidity of mathematics
makes it difficult to fully capture the richness and complexity of
human behaviour "). This is true, however I highlight how
financial mathematics is founded on reciprocity which is a component
of Justice, and this is the fundamental invariant not just in
finance, social systems in general but across any functionally
differentiated system. The mathematics of the Fundamental Theorem of
Asset Pricing is not involved in quantification but is concerned with
ensuring Justice.

On the basis of this definition of Justice the universe is Just,
since it works well as a complex, functionally differentiated system.
It is concerned with different things being in the correct balance
and is different from the idea that justice is based on everything
being the same, which might be characterised as a 'left-wing'
approach.

Now we can return to Taleb's account of "Antifragility"
that starts with

Antifragility is ... behind everything that has changed with time:
evolution, culture, ideas, revolutions, political systems,
technological innovation, cultural and economic success, corporate
survival, good recipes (say, chicken soup or steak tartare with a
drop of cognac), the rise of cities, cultures, legal systems,
equatorial forests, bacterial resistance … even our own existence
as a species on this planet. And antifragility determines the
boundary between what is living and organic (or complex), say, the
human body, and what is inert, say, a physical object like the
stapler on your desk.

This excerpt immediately raises the question: what is the difference
between antifragility and Socrates' conception of Justice.
Critically I have removed part of the text, which actually begins

Antifragility is beyond resilience or robustness. The resilient
resists shocks and stays the same; the antifragile gets better.

Suggesting the antifragile is about improvement, but I don't think
this establishes any clear water with the ancient philosophers.
Furthermore the argument that the best antidote to fragility is "skin
in the game" is not so different from the Enlightenment
attitude, espoused from Locke to Kant, that only property owners
could participate in democratic politics. The issue here, and
dominated British politics for much of the nineteenth century, was
that this excluded the majority from participating in democracy.
Taleb's conclusion refers to the Golden Rule "Do to others what
you want them to do to you".

These observations suggest that Taleb's argument in Antifragile is
close to mine in EQF. The difference is I focus on how the idea of
Justice is embedded in financial mathematics, why this is so and what
it implies. My conclusion is that in oredr to be able to manage
radically (Knightian/non-ergodic, etc.) uncertainty a broad range of
opinions need to be solicited and considered and so markets are
discursive arenas and must address truth, truthfulness and rightness.
Taleb suggests the essence of his book is "Everything gains or
loses from volatility. Fragility is what loses from volatility and
uncertainty." This seems a little trite to me, echoing the
actuary: "What has civilisation been worried about for 4,000
years?" The problem, as I see it , in Taleb's book is that he
leaves himself open criticisms captured in a paper
by Andrea Terzi (in what I would class as a 'left-wing' journal).
The point Terzi makes is

Taleb admits that the system cannot be made foolproof to BSE [Black
Swan events] but believes it can be made more resistant through some
form of economic and social Darwinism. His prescriptions include
consenting that what is fragile breaks early and never gets too big
to endanger the system should a BSE appear; letting economic players
who make errors be punished for their failures; not precluding
recessions from mopping up the system from the unfit to survival; and
not indulging in debt.

Taleb seems to have slipped into pseudo-Nietzschean philosophy that
distinguishes man and superman. He seems to identify with the
supermen and denigrates most scholars as 'imbeciles'. This view has
been supported in the evidence of responses supporting Taleb's attack
on Beard from, what look to me like, neo-Nazis. My concern is that I
feel the problems of finance, that Taleb purports to solve, are about
an obsession with identifying 'geniuses'
at the expense of deliberation and doubt.

I am not allowing comments on this article as I anticipate they will be dominated alt-right abuse.